Determination of the Boltzmann constant with cylindrical acoustic gas thermometry: new and previous results combined

Abstract

We report a new determination of the Boltzmann constant kB using a cylindrical acoustic gas thermometer. We determined the length of the copper cavity from measurements of its microwave resonance frequencies. This contrasts with our previous work (Zhang et al 2011 Int. J. Thermophys. 32 1297, Lin et al 2013 Metrologia 50 417, Feng et al 2015 Metrologia 52 S343) that determined the length of a different cavity using two-color optical interferometry. In this new study, the half-widths of the acoustic resonances are closer to their theoretical values than in our previous work. Despite significant changes in resonator design and the way in which the cylinder length is determined, the value of kB is substantially unchanged. We combined this result with our four previous results to calculate a global weighted mean of our kB determinations. The calculation follows CODATA’s method (Mohr and Taylor 2000 Rev. Mod. Phys. 72 351) for obtaining the weighted mean value of kB that accounts for the correlations among the measured quantities in this work and in our four previous determinations of kB. The weighted mean k̂B is 1.380 6484(28) × 10−23 J K−1 with the relative standard uncertainty of 2.0 × 10−6. The corresponding value of the universal gas constant is 8.314 459(17) J K−1 mol−1 with the relative standard uncertainty of 2.0 × 10−6.

High Accuracy When Measuring Physical Constants: From the Perspective of the Information-Theoretic Approach

“…−23 m 2 •kg•s −2 •K −1 [29] and k min = 1.3806484 × 10 −23 m 2 •kg•s −2 •K −1[32]. Then the comparative uncertainty ε LMTθF and the lowest relative uncertainty r LMTθF taking into account Equations (1), (6), (8),(10), and (16):…”

Speed of Sound of Gaseous Xenon in the Temperature Range from 308 to 370 K Measured with a Cylindrical Resonator

“…The speed of sound of xenon was measured with the fixed-path cylindrical acoustic resonator. A detailed description of the fundamental measurement principle and of the experimental apparatus has been given in our previous publications. − , In the following, a summarized description is presented.…”

“…In practice, the imperfections of the cavity perturbed the acoustic resonance field within the cavity, determined a shift of the resonant frequency, and contributed to the width of the resonance curve. In this work, the measured resonant frequencies were corrected for the perturbations from the thermal and viscosity boundary layers, the filling duct, the acoustic transducers, and the shell motions of the cavity with the correction models developed in our previous publications. ,, The thermal conductivity, viscosity, and the density of xenon that are needed as input properties of the correction models were calculated from the correlation functions from Refprop V10.0 and the EoS developed by Lemmon and Span . The perturbations from the shell motions were calculated with the approximate formulas developed in the our previous publications .…”

The Boltzmann Constant: Evaluation of Measurement Relative Uncertainty Using the Information Approach

“…The measurement data are summarized in Table 2. The noted scientific articles belong to CoP SI ≡ LMТΘF [14]- [20]. Although the authors of the research studies cited in these papers mentioned all the possible sources of uncertainty, the values of absolute and relative uncertainties can still differ by more than two times.…”

“…Following the IARU method, one can discuss the order of the desired value of the relative uncertainty belonging to CoP SI ≡ LMТΘF. An estimated observation interval of k is chosen as the difference in its values obtained from the experimental results of two projects: k max = 1.3806508 × [20]. In this case, the possible observed range S k of k placing is equal to:…”